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Simplify `12^2+12^2+12^2+......+12^2` Assume there are 12 of the 12^2. Please show...

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inquire123 | Student | eNoter

Posted June 8, 2013 at 7:08 AM via web

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Simplify `12^2+12^2+12^2+......+12^2`

Assume there are 12 of the 12^2.

Please show your workings clearly.Thanks

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mvcdc | Student , Undergraduate | (Level 1) Associate Educator

Posted June 8, 2013 at 7:38 AM (Answer #1)

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We start with:

`12^2 + 12^2 + ... + 12^2` , where we have 12 of the `12^2.`

Since we have 12 of each, we can re-write the expression:

`12^2 + 12^2 + 12^2 + 12^2 + 12^2 + 12^2 + 12^2 + 12^2 + 12^2 + 12^2 + 12^2 + 12^2` as:

`12 times 12^2`

Note that 12 is the same as `12^1`

Hence, 

`12^1 times 12^2` is `12^(1 + 2)` (since they have the same base, we can simply add the exponents. This then, simplifies to `12^3` (or 1728) . 

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jpeters55565 | High School Teacher | eNotes Newbie

Posted June 8, 2013 at 7:40 AM (Answer #2)

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we know 12^2 = 144.

There are 12 of the 12^2.

Multiplication is repeated addition.

Therefore, 12^2 + 12^2 + 12^2 ... + 12^2 = (12^2)(12)

which equals

12^3 = 1728

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